Do you need them for rt-pcr? Compared to what are you saying you didn't get good result? Trizol should be enough, just run the next step of your experiment and see. Maybe it's too early to say you don't have enough RNA.

The standard method is to collect blood samples in Paxgene or Tempus vacutainers specifically for blood RNA extraction. But if your blood samples are collected in regular anticoagulants, here are some methods for RNA extraction from whole blood.

For fresh whole blood:

Method 1:Prepare buffy coat then extract RNA from the the buffy coat using Trizol or other RNA extraction kits.